Simplify this question
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18
Qᴜᴇsᴛɪᴏɴ :-
Simplify :- 1/√[ 7 - 4√3]
Sᴏʟᴜᴛɪᴏɴ :-
→ 1/√[ 7 - 4√3]
Lets Try to Solve Denominator Root Part First ,
→ 7 - 4√3
Splitting The Terms, we can write ,
→ 4 + 3 - 2 * 2 * √3
→ (2)² + (√3)² - 2 * 2 * √3
comparing it with a² + b² - 2ab = (a - b)² we get,
→ (2 - √3)²
So,
→ √[2 - √3]²
we know that, (√a)² = a ,
→ (2 - √3)
Now, Our Question becomes :- 1/(2 - √3)
→ 1/(2 - √3)
Rationalizing The denominator we get,
→ 1/(2 - √3) * (2 + √3)/(2 + √3)
using (a + b)(a - b) = a² - b² in Denominator now,
→ (2 + √3) / [(2)² - (√3)²]
→ (2 + √3) / [ 4 - 3 ]
→ (2 + √3) / 1
→ (2 + √3) (Ans.)
Answered by
15
where x=2 and y=√3
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